Inspired by Einstein, I describe the passage from spatial geometry to spacetime geometry, (and the passage from spatial optimal transport to spacetime optimal transport) and the special role played by products with the real line.

A splitting theorem is a sufficient condition for recognizing such a product. An almost-splitting theorem is a sufficient condition for recognizing something that is nearly such a product.

I will then describe what appears to be first almost-splitting theorem in a spacetime setting.

Based on https://arxiv.org/abs/2610.10051.